Question

Total number of students in class B is 25% less than that of class A and the ratio of the number of boys in class A and B is 5:4 respectively. If the number of girls in class A and B is 60 and 40 respectively, then find the total number of students in class A?

• A. 180
• B. 140
• C. 120
• D. 160

Answer 1

The Correct Option is D

Let's find the total number of students in class A. Let the total number of students in class A be \( x \). According to the problem, the total number of students in class B is 25% less than in class A. Therefore, the number of students in class B is \( 0.75x \). 

Next, we are given the ratio of boys in class A to class B is 5:4. We also know the number of girls in these classes: 60 in class A and 40 in class B.

Let's denote the number of boys in class A as \( b_A \) and in class B as \( b_B \). So the equations for the total number of students can be written as:

\( b_A + 60 = x \) (Total students in A)

\( b_B + 40 = 0.75x \) (Total students in B)

From the boys' ratio \( \frac{b_A}{b_B} = \frac{5}{4} \), we get:

\( b_A = \frac{5}{4}b_B \)

Substitute \( b_A = x - 60 \) and \( b_B = 0.75x - 40 \) into the ratio equation:

\( x - 60 = \frac{5}{4} (0.75x - 40) \)

Simplifying, we have:

\( x - 60 = \frac{5}{4}(0.75x) - 50 \)

\( x - 60 = \frac{15}{8}x - 50 \)

To clear the fraction, multiply through by 8:

\( 8x - 480 = 15x - 400 \)

Rearranging gives:

\( 15x - 8x = 480 - 400 \)

\( 7x = 80 \)

\( x = 160 \)

The total number of students in class A is therefore 160.

Option	Total Students in Class A
180	Wrong
140	Wrong
120	Wrong
160	Correct